A study will be made of the kinetics of ion transport through ultrathin (biological and artificial) membranes which will involve innovation in both theory and experimentation. A general theory which unifies the continuum (Poisson-Nernst-Planck) and single jump (Eyring-Markin) approaches in a single, unified model will be developed. Our theoretical approach, illustrated with a specific, worked-out example in chapter II, will include carrier transport and ion adsorption effects. Two novel experimental techniques will be developed and used. Both are based on Fourier transformation. The first measures the membrane admittance simultaneously (rather than sequentially) at a large number of frequencies. Preliminary measurements (reported in chapter IV) demonstrate its feasibility and power. A second technique, covering the frequency range from 10 KHz to 10 MHz, is based on the voltage clamp method, but is not limited by the settling time of the potentiostat used. Methods of data analysis will be developed further along the lines of our recent work (see chapters VI and VII). These methods specifically take into account the dielectric membrane capacitance, and allow the separate, quantitative determination of diffusional, adsorption and phase transfer effects. Finally, the proposal enumerates a number of specific systems which will be investigated with the above-mentioned (and with more conventional) methods, and indicates why these measrements are important for our general understanding of the kinetics of ion transport through membranes.